Distance Metrics for Gamma Distributions

TL;DR

This paper derives analytic forms for key distance metrics between gamma distributions, including extensions and solutions, demonstrating their effectiveness in measuring distribution similarity.

Contribution

It introduces analytic formulas for the symmetrised Kullback-Leibler divergence and Kolmogorov-Smirnov statistic for gamma distributions, including an extension and intersection solution.

Findings

Analytic solutions for distance metrics between gamma distributions.

Demonstrated the metrics' effectiveness in distribution separability.

Provided practical examples illustrating metric similarities.

Abstract

Here I present the analytic form of two common distance metrics, the symmetrised Kullback-Leibler Divergence and the Kolmogorov-Smirnov statistic, as well as an extension of the Kolmogorov-Smirnov statistic for comparing theoretical gamma distributions. In doing so, I also present the analytic solution to the intersection of two gamma distributions. Lastly, I provide examples that demonstrate the similarity between these distance metrics and their usefulness in describing the separability of gamma distributions.